# The energetic cost of work extraction

**Authors:** Juliette Monsel, Marco Fellous-Asiani, Benjamin Huard, Alexia Auffèves  
**arXiv:** [1907.00812](https://arxiv.org/abs/1907.00812)  
**Date:** 2019-07-01  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1907.00812v3/

## Key points

- The study investigates work extraction from a qubit into a wave guide acting as a battery.
- The researchers focus on extracting work as the coherent component of the energy radiated by the qubit.
- The amount of extracted work is bounded by the qubit's ergotropy, representing its ability to perform useful work.
- The bound is saturated when the battery's charge reaches a certain threshold.
- Even with small battery charge, it is still possible to extract work based on quantum coherence initially injected into the qubit's state.
- This research presents a new scenario for studying quantum batteries using artificial qubits coupled to wave guides.
- It contributes to understanding quantum energy dynamics and optimizing energy utilization in quantum systems.

## Summary

In their study titled "The energetic cost of work extraction," authors Juliette Monsel, Marco Fellous-Asiani, Benjamin Huard, and Alexia Auffèves investigate the process of work extraction from a qubit into a wave guide (WG) acting as a battery. They focus on extracting work as the coherent component of the energy radiated by the qubit. The researchers stimulate this process by using a wave packet whose mean photon number can be adjusted to control the battery's charge. They demonstrate that the amount of extracted work is bounded by the qubit's ergotropy, which represents its ability to perform useful work. Furthermore, they find that this bound is saturated when the battery's charge reaches a certain threshold. Interestingly, even if the battery's charge is small, the study shows that it is still possible to extract work. The key factor in determining the amount of work that can be extracted in such cases is the quantum coherence initially injected into the qubit's state. This coherence serves as a crucial parameter when energetic resources are limited. This research presents a new and autonomous scenario for studying quantum batteries. It suggests that with current technology, state-of-the-art artificial qubits coupled to wave guides can be utilized to implement this framework. By exploring work extraction from qubits into wave guides acting as batteries, this study contributes to our understanding of quantum energy dynamics and provides insights into optimizing energy utilization in quantum systems. Overall, this refined summary highlights how Monsel et al. 's research investigates work extraction from qubits into wave guides acting as batteries. It emphasizes their findings regarding bounds on extracted work based on qubit ergotropy and highlights how quantum coherence plays a significant role in determining work extraction when energetic resources are limited.